Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.
Partially computed Groebner bases
Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
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i2 : I = ideal(random(3,R),random(3,R),random(3,R))
3 2 2 3 2
o2 = ideal (498a + 12901a b + 6847a*b + 14022b + 10510a c - 12117a*b*c -
------------------------------------------------------------------------
2 2 2 3 2
9968b c + 10467a*c - 15963b*c + 1331c - 14639a d + 14748a*b*d -
------------------------------------------------------------------------
2 2 2 2
5996b d - 189a*c*d - 4743b*c*d - 10539c d + 13098a*d + 6176b*d +
------------------------------------------------------------------------
2 3 2 2
12208c*d - 6837d - 1758a e + 10a*b*e + 497b e - 13104a*c*e - 6699b*c*e
------------------------------------------------------------------------
2 2 2
- 11311c e - 1573a*d*e - 11653b*d*e + 14456c*d*e + 1974d e - 6496a*e -
------------------------------------------------------------------------
2 2 2 3 3 2
15134b*e + 14640c*e - 14279d*e + 12857e , - 6465a - 2117a b +
------------------------------------------------------------------------
2 3 2 2 2
14162a*b - 4504b - 8964a c + 4276a*b*c - 12043b c + 4021a*c +
------------------------------------------------------------------------
2 3 2 2
5565b*c + 9384c - 1077a d + 15062a*b*d - 8045b d - 9652a*c*d -
------------------------------------------------------------------------
2 2 2 2 3 2
7872b*c*d + 8885c d - 12467a*d + 4614b*d - 2796c*d - 5066d + 7379a e
------------------------------------------------------------------------
2 2
- 10167a*b*e - 4104b e - 14200a*c*e - 4939b*c*e - 11132c e - 6504a*d*e +
------------------------------------------------------------------------
2 2 2 2
1920b*d*e + 10129c*d*e + 4060d e - 9339a*e + 3134b*e + 6148c*e -
------------------------------------------------------------------------
2 3 3 2 2 3 2
13334d*e - 4023e , - 2894a + 2822a b - 9560a*b - 1107b - 9841a c +
------------------------------------------------------------------------
2 2 2 3 2
5048a*b*c - 11201b c + 13114a*c + 4864b*c + 5638c + 13178a d +
------------------------------------------------------------------------
2 2 2
14103a*b*d + 11989b d + 78a*c*d + 8521b*c*d + 2607c d - 15167a*d +
------------------------------------------------------------------------
2 2 3 2 2
11335b*d + 15209c*d - 3766d + 12917a e - 1960a*b*e + 14733b e +
------------------------------------------------------------------------
2
2950a*c*e - 10099b*c*e - 9770c e - 1344a*d*e + 12542b*d*e - 5711c*d*e +
------------------------------------------------------------------------
2 2 2 2 2 3
15906d e - 14192a*e - 5806b*e + 6567c*e + 14887d*e + 1902e )
o2 : Ideal of R
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i3 : gens gb(I,PairLimit=>7);
1 7
o3 : Matrix R <--- R
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Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
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i5 : leadTerm gens g
o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o5 : Matrix R <--- R
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We can make a Groebner basis snapshot by using StopBeforeComputation, or
gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)
o6 = | ab2+9340b3-3772a2c-3993abc-3729b2c-143ac2-470bc2-1066c3+12735a2d-
------------------------------------------------------------------------
15822abd+6849b2d+1473acd-2776bcd-11743c2d+845ad2+15220bd2+12549cd2+
------------------------------------------------------------------------
2978d3+9578a2e+3201abe+6902b2e-11844ace-9562bce-8574c2e+7108ade+13908bde
------------------------------------------------------------------------
+1783cde-2677d2e-15285ae2+2464be2+14683ce2+3054de2-4244e3
------------------------------------------------------------------------
a2b+10749b3-13762a2c-6754abc-14874b2c-3103ac2-11017bc2-861c3+875a2d-
------------------------------------------------------------------------
4515abd-15099b2d+2957acd+961bcd+1307c2d-5566ad2-13997bd2+4381cd2-2137d3-
------------------------------------------------------------------------
13004a2e-13951abe+4821b2e-14880ace-10289bce+1975c2e-12765ade-4213bde-
------------------------------------------------------------------------
3858cde+4660d2e-15265ae2+9028be2+6952ce2+11654de2-6273e3
------------------------------------------------------------------------
a3+7971b3+4695a2c-3947abc-6395b2c-8817ac2+7661bc2+5732c3-15476a2d-
------------------------------------------------------------------------
11912abd-6223b2d+760acd-8330bcd+9909c2d-2032ad2-8782bd2-4532cd2-3206d3+
------------------------------------------------------------------------
4299a2e-14070abe+4621b2e-5398ace-305bce-136c2e+322ade-15399bde+3034cde+
------------------------------------------------------------------------
1881d2e-925ae2-64be2+3314ce2-4292de2-3267e3
------------------------------------------------------------------------
b3c+4967a2c2-2800abc2-5615b2c2+1793ac3-9479bc3+14918c4-10676b3d+
------------------------------------------------------------------------
13812a2cd-5456abcd+15857b2cd+3572ac2d-7642bc2d-7501c3d+4854a2d2-2393abd2
------------------------------------------------------------------------
+13597b2d2+8612acd2-3394bcd2-2725c2d2-14669ad3+2856bd3+1377cd3+6665d4-
------------------------------------------------------------------------
9713b3e+6372a2ce-8012abce+3016b2ce+4632ac2e-761bc2e+10130c3e-14219a2de+
------------------------------------------------------------------------
609abde+3592b2de+5757acde-12653bcde+7173c2de-8779ad2e-5567bd2e+3334cd2e-
------------------------------------------------------------------------
4952d3e-15899a2e2+7884abe2-12387b2e2+7298ace2+11864bce2-13073c2e2-
------------------------------------------------------------------------
8251ade2-11095bde2-10851cde2-11197d2e2-9156ae3-1038be3-12908ce3-7881de3+
------------------------------------------------------------------------
11188e4 b4+7110a2c2-1742abc2-12249b2c2-7959ac3+6250bc3-7512c4+4970b3d-
------------------------------------------------------------------------
14831a2cd+6357abcd-10793b2cd+14435ac2d-6885bc2d-4261c3d-13827a2d2+
------------------------------------------------------------------------
11737abd2-15895b2d2+6684acd2+1488bcd2+5868c2d2+9025ad3-9711bd3+12204cd3+
------------------------------------------------------------------------
5117d4-10875b3e-15875a2ce+13260abce+13964b2ce-14260ac2e+7766bc2e-572c3e+
------------------------------------------------------------------------
6542a2de-12286abde-2722b2de-7451acde-14908bcde-2257c2de-4361ad2e+
------------------------------------------------------------------------
12592bd2e+15731cd2e+4954d3e-13644a2e2+11272abe2+14744b2e2-3441ace2-
------------------------------------------------------------------------
2674bce2-1864c2e2+2063ade2-394bde2-4906cde2-5482d2e2+4624ae3-11499be3+
------------------------------------------------------------------------
15898ce3+9995de3+13616e4
------------------------------------------------------------------------
abc3-3415b2c3+15032ac4-9163bc4-11054c5-4750a2c2d-2208abc2d+13641b2c2d+
------------------------------------------------------------------------
646ac3d+14266bc3d+1014c4d-9036b3d2-4213a2cd2+11136abcd2+526b2cd2+
------------------------------------------------------------------------
9850ac2d2-15509bc2d2+14988c3d2-11510a2d3+6468abd3+3072b2d3-10236acd3+
------------------------------------------------------------------------
13289bcd3+3550c2d3+1271ad4+10962bd4+13537cd4+5193d5+13698a2c2e+
------------------------------------------------------------------------
13334abc2e+3515b2c2e+11992ac3e-9434bc3e-4937c4e+11762b3de-5133a2cde-
------------------------------------------------------------------------
10827abcde-11962b2cde+11598ac2de+8031bc2de-6089c3de-15199a2d2e+
------------------------------------------------------------------------
13255abd2e+10822b2d2e+905acd2e-6053bcd2e-11580c2d2e-1585ad3e-8640bd3e+
------------------------------------------------------------------------
7709cd3e-13926d4e+15370b3e2+14501a2ce2-13716abce2-13523b2ce2+11345ac2e2-
------------------------------------------------------------------------
3210bc2e2-8734c3e2+3810a2de2+2094abde2+7680b2de2+14130acde2+736bcde2-
------------------------------------------------------------------------
7016c2de2+11775ad2e2-7236bd2e2-11680cd2e2-5740d3e2+15981a2e3+8793abe3-
------------------------------------------------------------------------
2490b2e3+10390ace3+7461bce3-15910c2e3+1926ade3+5716bde3+9737cde3-
------------------------------------------------------------------------
12555d2e3+5992ae4+7157be4-10173ce4+7063de4-14617e5
------------------------------------------------------------------------
a2c3+12993b2c3+6203ac4-1823bc4+7109c5+6532a2c2d-12631abc2d-9976b2c2d-
------------------------------------------------------------------------
8117ac3d-12539bc3d+3652c4d+9273b3d2+2861a2cd2-12911abcd2+5657b2cd2-
------------------------------------------------------------------------
14727ac2d2-13364bc2d2+10093c3d2+11554a2d3-5513abd3+10581b2d3+9690acd3-
------------------------------------------------------------------------
11120bcd3-12690c2d3-7253ad4-507bd4-9410cd4+4650d5-15436a2c2e+3636abc2e-
------------------------------------------------------------------------
13454b2c2e+9532ac3e+4058bc3e+14775c4e+7935b3de-3158a2cde-2764abcde-
------------------------------------------------------------------------
11754b2cde-7637ac2de+2876bc2de-5888c3de+3671a2d2e+3761abd2e+2410b2d2e+
------------------------------------------------------------------------
6015acd2e+15490bcd2e-5902c2d2e+11358ad3e+14213bd3e+10365cd3e-13287d4e+
------------------------------------------------------------------------
9549b3e2-8869a2ce2+8079abce2-14436b2ce2+9549ac2e2+15592bc2e2+15598c3e2+
------------------------------------------------------------------------
183a2de2+9289abde2+3455b2de2-12910acde2-459bcde2-13755c2de2-6770ad2e2-
------------------------------------------------------------------------
9390bd2e2+2508cd2e2-8384d3e2+15310a2e3-8285abe3+9025b2e3+12968ace3+
------------------------------------------------------------------------
13592bce3-6904c2e3-1644ade3-4139bde3-638cde3-15179d2e3+8567ae4+179be4-
------------------------------------------------------------------------
6111ce4-5115de4+5990e5 |
1 7
o6 : Matrix R <--- R
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i7 : leadTerm gbSnapshot(I)
o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |
1 7
o7 : Matrix R <--- R
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